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Implicit Analytic Solution of Michaelis-Menten-Monod Kinetics.

Federico Maggi¹, Daniele la Cecilia¹

¹School of Civil Engineering, The University of Sydney, Blvd. J05, Sydney 2006, New South Wales, Australia.

|August 29, 2019

Summary

A new analytic solution for enzyme kinetics, based on the Michaelis-Menten-Monod model, provides substrate and enzyme concentrations without numerical methods. This method accurately predicts nitrification rates in microbial communities.

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Area of Science:

Biochemistry
Microbial Ecology
Chemical Engineering

Background:

Enzyme kinetics are often described by the Michaelis-Menten-Monod model.
Solving these models typically requires numerical integration or iterative methods due to transcendental functions.
This complexity can hinder real-time analysis and direct calculation of reaction components.

Purpose of the Study:

To present an analytic solution for enzyme kinetics within the Michaelis-Menten-Monod framework.
To enable direct calculation of substrate, enzyme, and microbial biomass concentrations.
To eliminate the need for numerical integration or iterative solvers.

Main Methods:

Developed an analytic solution where time is replaced by product concentration.
The solution implicitly solves for substrate, enzyme, and microbial biomass.
Validated the solution using experimental data of NO2- nitrification by Candidatus Nitrospira defluvii.

Main Results:

The analytic solution accurately predicts substrate, enzyme, and biomass concentrations across all time domains.
Experimental validation showed excellent agreement between the analytic solution and finite difference numerical methods.
Correlation coefficients exceeded 0.99 with residuals below 2.75%.

Conclusions:

The presented analytic solution offers a direct and efficient method for analyzing enzyme kinetics.
This approach simplifies the study of microbial processes like nitrification.
The method provides a robust alternative to traditional numerical techniques for kinetic modeling.